Answer
$63$
Work Step by Step
From part (a): $a_n= a_1 r^{n-1}$ ...(1)
Here, we have Common Ratio $r=\dfrac{1}{2}$ and first term $a_1=32$
Equation (1) gives: $a_n=32 \times (\dfrac{1}{2})^{n-1}$
This implies that $n = 6$
We know that $S_{n}=a_1(\dfrac{1-r^{n}}{1-r})$
Now, $S_{6}=32 \times (\dfrac{1-(1/2)^{n}}{1-\dfrac{1}{2}})$
$S_{6}=32 \times (\dfrac{1-(1/2)^{n}}{-\dfrac{1}{2}})$
Hence, $S_{6}=63$
